7.EE.4: Two-Step Equations and Inequalities
Also written as 7.EE.B.4 and CCSS.MATH.CONTENT.7.EE.B.4 · Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
The Official Wording
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Common Core State Standards, Grade 7, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 7.EE.4 Means in Plain English
Seventh graders write and solve two-step equations like 3x + 12 = 25.50: a $12 case plus 3 screen protectors costs $25.50, so each protector is $4.50. Forms like 2(x + 6) = 54 count too, and the arithmetic route, subtract then divide, uses the same steps.
Inequalities solve the same way: an $8 pass plus $6 a movie, under $50, gives 6m + 8 < 50, so m < 7, an open circle at 7 and at most 6 movies. Equations with x on both sides wait for 8th grade (8.EE.7).
7.EE.4 I Can Statements
- I can write a two-step equation or inequality for a word problem.
- I can solve two-step equations like 3x + 12 = 25.50.
- I can graph an inequality’s solutions and explain what they mean.
7.EE.4 Worked Example
A budget with a fixed cost and a per-student cost: a two-step inequality, its graph, and the moment a decimal answer meets a class of real children.
A field trip costs $140 for the bus plus $12.50 per student for museum tickets. The total must stay under $500. Write and solve an inequality for the number of students, graph it, and say what the solutions mean.
- Let n be the number of students. The bus is a fixed $140, each student adds $12.50, and the total must be less than $500.12.50n + 140 < 500
- Undo the addition first: subtract 140 from both sides. The inequality sign stays the same.12.50n < 360
- Undo the multiplication: divide both sides by 12.50. It is a positive number, so the sign still stays.n < 28.8
- Graph it: an open circle at 28.8, because 28.8 itself is not allowed, and an arrow to the left.Open circle at 28.8, shaded to the left
- Read the graph in context. n counts students, so only whole numbers from 0 to 28 make sense.Up to 28 students can go
Check it: Test the edges: 28 students cost 12.50 × 28 + 140 = 350 + 140 = $490, under $500. 29 students cost $502.50, over budget.
Common Mistakes with 7.EE.4
Undoing in the wrong order
3x + 12 = 25.50: 25.50 ÷ 3 = 8.50, then 8.50 - 12 = -3.50
Try this: Undo the last operation first. In 3x + 12, the 12 was added last, so subtract 12 before dividing by 3.
Distributing to one term of p(x + q)
4(x + 2.50) = 62, so 4x + 2.50 = 62
Try this: Divide both sides by 4: x + 2.50 = 15.50, so x = 13. Or distribute to both terms: 4x + 10 = 62.
Rounding 28.8 up to 29
n < 28.8, so 29 students can go
Try this: Round in the direction the inequality allows: 29 students cost $502.50, over budget, so the answer is at most 28.
Where 7.EE.4 Fits
Practice 7.EE.4
Quick Check
- Solve 5x - 7 = 18.
- Solve 3(y + 4.5) = 21.
- A tutor charges $20 plus $15 an hour, and you can spend less than $95. Write and solve an inequality for the hours h.